Method for deconvolution of non-ideal frequency response of pipe structures to acoustic signals

ABSTRACT

A method of deconcolving the non-ideal frequency response from acoustic vibrations transmitted along a structure such as a drill string is disclosed. The deconvolution retains the values of the transmission time between the signal source and the receiver, in the form of an exponential phase term, and is multiplied by the amplitude frequency response of the structure. The input data time series, after transformation into the frequency domain, is then divided by the deconvolution operator. The deconvolution method may be used in a noise reduction method where both axial and torsional vibrations are generated from the same location, where one of the time series is shifted by the amount of the time delay, so that the vibrations generated from the same location coincide, providing reinforcement of the desired signal. The deconvolution method may thus be used in determining a seismic source signature in prospecting where a drill bit is the source, in analyzing drilling parameters from drill string vibrations, and in stress wave telemetry, and also in leak detection.

This application is a continuation-in-part of my copending applicationSer. No. 564,621, which was filed Aug. 8, 1990 and is assigned toAtlantic Richfield Company.

This invention is in the field of signal processing, and is morespecifically directed to reducing distortion in acoustic signalstraveling along a pipe structure.

BACKGROUND OF THE INVENTION

In the petroleum industry, acoustic vibrations along structures such asdrill strings, pipelines, and the like have been found to be a usefulcarrier of information. As will be further noted hereinbelow, both inthe drilling of wells and in the transmission of fluids through apipeline, interpretation of the vibrations which are generated by adrill or by leaks can provide important information concerning theenvironment and operation of the structure. In addition, activegeneration of acoustic vibrations can be used for transmission ofinformation along such structures at reasonable data rates. The instantinvention is directed to improving the ability to interpret acousticvibrations in order to retrieve the desired information.

One application in which the interpretation of acoustic vibrations canprovide important information is during the drilling of both land andoffshore wells, in the exploration for and production of petroleumproducts. Over the years, the more readily found and accessiblepetroleum reservoirs have of course been discovered and depleted first.As a result, the exploration and production operations must necessarilyconcentrate to a greater degree on less accessible and less readilydiscoverable reserves. In order to reach these locations, the depths ofdrilling have increased, the locations at which drilling takes placehave become increasingly difficult and less accessible, and the drillingoperations have necessarily become more complex. Accordingly, drillingoperations in the search for and production of petroleum products havebecome more expensive, with this trend likely to continue in the future.Because of this increasing cost, the accuracy and efficiency of thedrilling operation is becoming even more important.

The success and efficiency of the drilling operation depends to a largedegree on the quantity and quality of information that the drillingoperator has about the sub-surface structure into which the drilling istaking place, and also about parameters concerning the operation of thedrill bit as it proceeds into the earth. Many techniques for acquisitionand communication of such information have been tried and used in theindustry. Recent work has been done, as will be discussed hereinbelow,in acquiring information from the acoustic vibrations of the drillstring itself during drilling. In such an application, the drill stringserves not only to power and guide the drilling, but also as acommunication medium for such acoustic signals. These signals areinherently generated during the drilling operation and communicated viathe drill string to detectors. Analysis of the signals providesinformation about the drilling parameters and the drilling operationitself, and also about the geology into which the drilling is takingplace.

An example of a system and method using acoustic vibrations transmittedalong the drill string itself to communicate various drilling parametersis described in U.S. Pat. No. 4,715,451, issued Dec. 29, 1987, assignedto Atlantic Richfield Company, said U.S. Patent incorporated herein bythis reference. This system measures the motion of, and the strains on,a drillstem in various directions, by way of monitoring such indicationsas axial, torsional and lateral vibrations, and deflections of thedrillstring. The strain generated on the drill string during drilling isindicative of such factors as the impact and rotation of the drill bit,its interaction with the formation into which the drilling is takingplace, and the interaction with portions of the drill string above thebit with the surrounding formation. In this system, measurements aremade by way of detectors, such as accelerometers and strain gages, whichare located in a sub near the top of the drill string and which generateelectrical signals corresponding to the vibration and motion detectedthereby. Analysis of the electrical signals provides real-timeinformation on parameters such as drillstem vibration and deflection,the location of interaction between the casing and the drillstem, thespeed of and load on the drill bit, and other drill bit operatingcharacteristics. Such real-time operating information is quite useful inefficiently and accurately performing the drilling operation.

As disclosed in said U.S. Pat. No. 4,715,451 at column 5, lines 59through 68, in Rector III, et al., "Extending VSP to 3-D and MWD: Usingthe drill bit as downhole seismic source", Oil and Gas Journal, (Jun.19, 1989), pp. 55-58, and in Rector, Marion and Widrow, "Use ofDrill-Bit Energy as a Downhole Seismic Source", 58the InternationalMeeting of SEG, paper DEV 2.7, pp. 161-164, analysis of the vibrationscommunicated along th drill string during drilling is also useful in theseismic prospecting area, where the vibrations generated by the drillbit into the earth are the seismic source signals. In the TOMEX®(Trademark of Western Atlas International Inc.) system disclosed byRector III et al., seismic detectors such as geophones or hydrophonesdetect the reflections of these vibrations near the surface at alocation distant from the drilling operation. Detection of thevibrations at the wellhead, as communicated by the drill string, canprovide a signature of the source vibrations. Conventionalcross-correlation of the vibrations detected by the geophones orhydrophones with the source vibrations communicated through the drillstring provides data concerning the location of sub-surface strata andinterfaces.

Another system which utilizes the drill string as a medium for thetransmission of data is referred to as stress wave telemetry. Stresswave telemetry systems are disclosed in copending U.S. patentapplications Ser. No. 188,231 filed Apr. 21, 1988, now U.S. Pat. No.4,992,997, issued Feb. 12, 1991, Ser. No. 554,030 filed Jul. 16, 1990,and in Ser. No. 554,022 Jul. 16, 1990, all applications assigned toAtlantic Richfield Company, and incorporated herein by this reference.These systems include transmitters, such as solenoids, eccentric motors,and piezoelectric transducers, which intentionally vibrate the drillstring in a manner corresponding to the desired data. This data mayinclude information concerning drilling parameters, such as in theabove-referenced U.S. Pat. No. 4,715,451. In the case of stress wavetelemetry, however, the information is not extrapolated from analyzingthe naturally occurring vibrations, but vibrations are generated whichare in addition to the naturally occurring vibrations, these generatedvibrations corresponding to the drilling parameter and other informationtransmitted along the drill string.

Another important application utilizing the transmission of acousticsignals along a pipe structure is leakage detection. An example of asystem and method using acoustic signals for leakage detection in a pipeis described in my copending application Ser. No. 391,919, filed Aug.10, 1989 and assigned to Atlantic Richfield Company. As describedtherein, the leakage of fluids from within the pipe through a crack orfaulty joint in the pipe generates acoustic vibrations in the pipe. Thesystem and method described in said copending application Ser. No.391,919 identifies the existence and location of such leaks by analysisof these acoustic vibrations, for example by measuring selectedcombinations of axial and torsional vibrations and fluid pressurefluctuations at a point along the pipe.

It has been discovered, however, that vibrations, whether from the drillbit, from stress wave telemetry transmitters, or from leaks, are notcommunicated through the drill string in an ideal manner, due to thenon-ideal response of the drill string to such vibrations. As describedin Drumheller, "Acoustical Properties of Drillstrings", J. AcousticSociety of America, 85(3) (March, 1989), pp. 1048-1064, conventionaldrill strings, which consist of a number of lengths of drill pipe joinedby pipe joints, inherently have frequency domain stopbands or deadbandswhich attenuate acoustical signals at the stopband frequencies. Thisfrequency-dependent attenuation can severely distort some signals. Whilesimple deconvolution of the reflective effects of the ends of the drillstring and the bottomhole assembly has been done, such deconvolution hasaccounted only for effects dependent upon the total length of the drillstring and the construction of the bottomhole assemble, and has notaccounted for the frequency dependent transmission of the drill stringdue to such factors as the tool joints between sections of the drillstring.

It is therefore an object of this invention to provide a method ofreducing the effects of the frequency response on informationcommunicated along a pipe structure such as a drill string, productiontubing, or pipeline.

It is a further object of this invention to provide such a method whichincludes deconvolution of the pipe string response in accomplishing thenoise reduction.

It is a further object of this invention to provide such a method wherethe deconvolution takes into account the passbands and deadbands of ajointed pipe structure.

It is a further object of this invention to provide such a method whichstores time delay values of the signals.

It is a further object of this invention to provide such a method wherethe Fourier transform of the impulse response may be performed andstored, using a small number of points, with no loss of information.

Other objects and advantages of the invention will be apparent to thoseof ordinary skill in the art having reference to this specification,together with the drawings.

SUMMARY OF THE INVENTION

The invention may be incorporated into a method for deconvolving thenon-ideal frequency response of a structure, such as a pipeline or drillstring, from acoustic signals transmitted therealong. The frequencyresponse is measured or modeled, and stored in a computer memory. A timedelay value (or plural values, if signals of different velocities are tobe deconvolved) may be calculated according to the travel velocities anddistances, and stored; the time delay value corresponds to the traveltime of the signal from its source to the sensor location, and, for usein the frequency domain, is expressed as an exponential term. A Fouriertransform is performed over a portion of the input data corresponding tothe time period of interest. Deconvolution is performed by dividing thefrequency domain representation of the input data by the frequencyresponse. If the time delay values are used, these values may beadjusted to examine a different source location, for example in the caseof noise reduction by addition of compressional and torsional signals,or in leak detection.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a drilling operation, illustrating anapplication of the embodiment of the invention.

FIG. 2 is a flow chart illustrating a method in which the preferredembodiment of the invention may be used.

FIG. 3a is a time domain representation of a source signal transmittedinto the drill string of FIG. 1.

FIGS. 3b and 3c are time domain representations of axial and torsionalvibrations, respectively, measured at the top of the drill string ofFIG. 1, illustrating both signal and noise, responsive to the sourcesignal of FIG. 3a.

FIGS. 4a and 4b are frequency domain representations of the impulseresponse of a drill string to axial and torsional vibrations,respectively.

FIG. 5 is a flow diagram of a preferred method of deconvolutionaccording to this embodiment of the invention.

FIGS. 6a and 6b are time domain representations of axial and torsionalvibrations, respectively, measured at the top of the drill string ofFIG. 1, after deconvolution.

FIGS. 7a and 7b illustrate the time shifting of the axial vibrationrepresentation and torsional vibration representation of FIGS. 6a and 6brelative to one another.

FIG. 8 is an electrical diagram, in block form, of a computing systemfor receiving and processing method according to the preferredembodiment of the invention.

FIG. 9 is a flow chart of a method of deconvolution according to anotherembodiment of the invention.

FIGS. 10a and 10b are time-domain plots of FSK data before and afterdeconvolution according to the method of FIG. 9

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

It should be noted that the deconvolution method according to thepreferred embodiment of the invention will be described hereinbelowprimarily in the context of a method for reducing noise in the acousticsignals generated by a drill bit during drilling, as described in saidcopending application Ser. No. 564,621 filed Aug. 8, 1990, incorporatedherein by this reference. As will be described hereinbelow, however, thedeconvolution method according to the preferred embodiment of theinvention is also applicable to and beneficial in other applications ofacoustic wave transmission along a structure, such as stress wavetelemetry, leakage detection, and the like.

Seismic Exploration Using the Drill Bit as a Seismic Source

Referring now to FIG. 1, a drilling operation with which a preferredembodiment of the invention is used will be described. A conventionaldrilling rig 2 is shown as powering drill string 4, which conventionallyconsists of multiple sections 6 of drill pipe. Sections 6 are connectedto one another by tool joints 8 in the conventional manner. Drill bit 10is connected at the distal end of drill string 4, and can be a rotarybit, jet or spud bit, or other type of drill bit conventional in theart. As shown in FIG. 1, drill bit 10 is connected to bottomholeassembly 11, which in turn is connected to sections 6 of drill string 4.Provision of such a bottomhole assembly 11 is conventional in thedrilling art, and is the usual location of detectors for sensingattributes of the drilling operation, as well as for other conventionalfunctions. While such a bottomhole assembly 11 is shown in FIG. 1 and isalmost always used in petroleum exploration drilling, it should be notedthat the presence of bottomhole assembly 11 is not required, dependingupon the particular drilling operation being performed. However, forpurposes of stress wave telemetry as will be described hereinbelow,transducers for vibrating drill string 4, according to information to betransmitted from downhole to the surface, are preferably located in sucha bottomhole assembly 11.

It is contemplated that the rotary bit, due to its mode of operation indrilling, will generate quite complex vibrational information, suchinformation being transmitted, and capable of being subsequentlyanalyzed as described herein. The vibrational information includes bothaxial compressional vibrations and torsional vibrations in drill string4, such vibrations being generated by the powering of drill bit 10 andits interaction (as well as the interaction of drill string 4) with theformations encountered in the earth. The powering of drill bit 10, ofwhatever type, can be done either from the surface or via a downholemotor, according to the type of drill bit 10 used and the particulardrilling operation undertaken.

Sub 12 is connected within drill string 4 near the surface of the earth.Sub 12 contains detectors, such as accelerometers, strain gages,piezoelectric transducers, and the like, for detecting vibrations indrill string 4 and generating a signal, such as an electrical signal,corresponding to the detected vibrations. Examples of such detectors andtheir placement in sub 12 are described in U.S. Pat. No. No. 4,715,451issued Dec. 29, 1987, assigned to the Atlantic Richfield Company, andincorporated herein by this reference. Since both axial and torsionalvibrations are detected and used in the analysis, such detectors mustaccordingly be placed and oriented to detect both axial and torsionalvibrations. The electrical signals generated from the detectors withinsub 12 are communicated to computer system 19 for analysis of thesignals corresponding to the vibrations of drill string 4, as will bedescribed hereinbelow.

As described in said U.S. Pat. No. No. 4,715,451, the vibrationsdetected by the detectors in sub 12 are representative of certaindrilling parameters. Analysis of these vibrations, as communicatedelectrically from the detectors in sub 12, can quantify these drillingparameters, assuming that those vibrations from drill bit -0 can besufficiently separated from such other vibrations along drill string 4which are not generated from drill bit 10. Accordingly, an importantapplication of this method is the reduction of the effects of thevibrations from sources not of interest (i.e., the "noise") on thevibrations generated by the operation of drill bit 10 and drill string 4on the sub-surface formations which are of interest (i.e., the"signal"). As a result of such improvement of the signal-to-noise ratio,it is contemplated that the drilling operation can be more efficientlyperformed and controlled, as the quality of real-time information aboutimportant drilling parameters is improved by the use of this method.

Alternatively, or in addition, to the above utilization of thisinformation, the vibrations sensed by detectors in sub 12 can be used inseismic prospecting. As described in the Rector III et al. article citedhereinabove, the vibrations generated by drill bit 10 during thedrilling operation are transmitted through the earth. It is believedthat the vibrations which are transmitted axially along drill string 4from drill bit 10 correspond to pressure ("P") waves which drill bit 10imparts into the earth. These vibrations, when reflected below thesurface of the earth and received at locations remote from the drillingoperation, are indicative of the attributes of these sub-surface strataand their interfaces.

As shown in FIG. 1, the vibrations generated by drill bit 10 aretransmitted acoustically through the earth. For example, vibrations mayfollow path 15 downwardly from drill bit 10, reflecting from interface12 between strata 14 and 16 to the surface, at which the vibrations aredetected by detector 18. Vibrations may also directly travel from drillbit 10 along path 13 to detector 18. Detector 18 may be a conventionalgeophone, or other conventional apparatus useful in the detection ofvibrations at the surface of the earth (or water, as the case may be).While a single detector 18 is illustrated in FIG. 1, it should be notedthat, of course, multiple detectors 18 are conventionally placed alongthe surface of the earth during seismic prospecting. The use of an arrayof multiple detectors 18 provides detailed information about thesub-surface geology of the region under analysis. The analysis of thedetected vibrations by each of such multiple detectors 18 is done inmuch the same manner as for a single detector 18, with the differencesin travel times among the detectors 18 in the array indicative of thestrata and interfaces at different locations. The vibrations detected bydetector 18, as well as those detected by detectors in sub 12, arecommunicated in the conventional manner via field electronics 21 tocomputer system 19 for analysis according to the method to be describedhereinbelow.

As described in the article by Rector III, et al. cited hereinabove,seismic prospecting using drill bit 10 as the seismic source, as withany seismic source, requires knowledge of the input signal so thatreflections and other information can be gleaned from the reflectedsignal received by geophone 18. Conventional methods, such ascross-correlation of the received signal with the input signal as in thewell-known Vibroseis® (Registered trademark of Continental Oil Company)technique, and performed by computing system 19 either on location inthe field, or alternatively at an off-site computing center, identifysuch important parameters in the received information such as transittime from the source (i.e,. drill bit 10) to the geophone 18, which willindicate the acoustic velocities and locations of reflecting strata.

Noise Reduction for Acoustic Signals

However, where drill bit 10 is the seismic source and where detectors,for example in sub 12, are used to measure the source signal astransmitted through drill string 4, the vibrations received viatransmission through drill string 4 will include any effects of theresponse of the drill string 4 upon the vibrations generated by drillbit 10. As noted in the Drumheller article noted hereinabove, theresponse of a drill string to vibrations passing therethrough is suchthat severe distortions of the acoustic signal will occur as the signaltravels to and is received by the detectors in sub 12, at or near thesurface of the earth. In the seismic prospecting application, it shouldbe noted that the signal received by geophone 18 will not have thedistortions generated by the acoustic response of drill string 4, butwill be subject to distortions presented by the earth. Of course, in theseismic prospecting application, such distortions are the veryinformation which is sought by the process, as the distortions (e.g.,reflections) correspond to the geology of the drilling location.Furthermore, as noted hereinabove, the vibrations from drill bit 10which are transmitted along drill string 4 will have superimposedthereupon such "noise" vibrations resulting from the flow of drillingmud at high pressure, and the operation of various mechanical elementson drill string 4, as discussed hereinabove.

As is well known in the field of seismic prospecting, correlationtechniques determine the time delay between the source signal and thereceipt of the reflected signal; from this time delay, the depth andlocation of reflecting strata and interfaces between strata can becalculated. The accuracy of these calculations depends upon how well theanalysis can recognize the point in time at which the reflected signalis detected. Due to the presence of noise in the measurements, as wellas the weakness of the seismic signal, especially those resulting frompartial reflections from very deep strata, this identification of thereceipt of the measured signal is often not easily accomplished. Thisprocess is made even more difficult where the signature of the sourcesignal is not known, is distorted, or is otherwise inaccurate due toadditional noise superimposed thereupon. As noted above, where thevibrations are distorted in transmission through drill string 4 in a wayin which the vibrations traveling through the earth are not distorted,and where significant noise is generated by the flow of drilling mud andother mechanical interactions, the ability to accurately cross-correlatethe source signal with the reflected waveforms becomes even morereduced.

Also as noted above, stress wave telemetry is another application inwhich vibrations of a drill string 4 are analyzed for theirinformational content. Of course, whether the signals are inherent inthe vibrations generated during drilling, as discussed above, or inducedby additional equipment such as transducers located in downhole assembly11 as in the case of stress wave telemetry, noise and distortion of thesignal occur during transmission through drill string 4. Furthermore,considering the amplitude of signals which can be generated by downholetransducer apparatus as are described in said copending application Ser.No. 183,231 filed Apr. 21, 1988, where such transmitting apparatus is oflimited size and power due to its installation downhole, signal-to-noiseratio and distortion is a serious problem, even where the frequencies oftransmission may be known in advance, as is the case in stress wavetelemetry.

Referring now to FIG. 2, a method for reducing the effects of noise ondetected vibrations transmitted through a pipe structure such as drillstring 4 will now be described. The method begins at process 20, atwhich both axial and torsional vibrations in drill string 4 are measuredby detectors in sub 12 near the surface of drill string 4. As describedhereinabove, these detectors are conventional accelerometers, straingages, piezoelectric transducers and the like; an example of a systemincluding such detectors is described in the above-referenced U.S. Pat.No. 4,715,451.

It is contemplated that conventional computer equipment, programmed maybe used to perform the noise reduction and deconvolution methodsdescribed herein. An example of a conventional computer systemparticularly adapted to the task of seismic prospecting using the drillbit as a seismic source is the TOMEX® Field System manufactured and soldby Western Atlas International. Other conventional computer systems suchas microcomputer-based workstations may of course be used in performingthis method, as well. In particular, certain special purposemicroprocessor circuits, commonly referred to as digital signalprocessors (DSPs), are constructed to rapidly perform operations usefulin digitally performing Fourier transforms, such transforms accomplishedaccording to the class of methods conventionally referred to as DiscreteFourier Transforms (DFTs), an important type of which are commonlyreferred to as Fast Fourier Transforms (FFTs). Readily available add-oncircuit boards containing such DSP processors, for use in amicrocomputer-based workstation, are particularly well-suited forperforming the process steps of FIG. 2, including the deconvolutionoperation discussed herein.

Referring to FIG. 8, a block diagram of an example of a computing system19 for performing the analysis described herein is shown. Computingsystem 19 of FIG. 8 receives information both fromd etectors in sub 12,and also from geophones 18 via field electronics 21, and accordinly isapplicable for analysis of information from seismic prospecting wheredrill bit 10 is the seismic source and geophones 18 receive thereflected signals, as in FIG. 1. Of course, computing system 19 may beconstructed to receive only input from detectors in sub 12, foranalyzing vibrations in drill string 4 to determine certain drillingparameters, or in the stress wave telemetry application, as describedhereinabove.

Detectors in sub 12 provide analog electrical input responsive totorsional and axial vibrations detected in drill string 4, toanalog-to-digital converters (ADC) 82. ADCs 82 convert the analogsignals received from each of the detectors in sub 12 into digital formin the conventional manner. ADCs 82 communicate the digitalrepresentations fo the vibrations, either from each of the detectors orin a multiplexed manner, to coding circuit 84 which converts the digitaldata into signals suitable for transmission to computing system 19. Theconversion by coding circuit 84 is according to conventional datatransmission techniques, for example by coding the information intofrequency shift keyed (FSK) digital data, phase shift keyed (PSK)digital data, or another conventional coding scheme. Coding circuit 84then transmits the coded information concerning the vibrations detectedat sub 12 to computing system 19; such transmission may be by way ofsynchronous digital data transmission, or by microwave or infraredtransmission, all of which being conventional for the transmission ofdigital data.

Similarly, field electronics 21 includes ADCs 86 for receiving anddigitizing analog signals received from geophones 18. ADCs 86communicate the digital signals to multiplexer and coding circuit 88,which multiplexes the data received from the multiple geophones 18, andtransmits the data to computing system in similar manner as codingcircuit 84 described hereinabove. As noted above, in the stress wavetelemetry and drilling parameter communication applications, fieldelectronics 21 need not be provided, as no inputs from geophones 18 arenecessary in such analysis.

Computing system 19 includes interface 90 for receiving the coded andtransmitted signals from coding circuit 84 and from multiplexer andcoding circuit 88, and for communicating the received signals tocomputer 92 in a manner which can be stored and manipulated thereby.Computer 92 is a conventional high speed PCbased workstation, forexample based on 80386 or 80486 microprocessors. Due to the nature ofthe method to be described hereinbelow, it is also preferable thatcomputer 92 include one or more DSP add-on boards as described above; apreferred DSP board is the Spirit 30 DSP board manufactured and sold bySonitec. Computer 92, as mentioned above, includes conventionalhardware, including the DSP boards, but is programmed to perform theanalysis to be described hereinbelow. Computer 92 may be connected tomonitor 94, tape drive 96, printer 98 or interface 99, for communicationand storage of the results in the conventional manner.

It should be noted that the time series of vibrational signals which areanalyzed by this method may be a continuing series of signals, so thatthe analysis occurs periodically, but on substantially a real-timebasis. Computing system 19 thus can be located in the field foriterative analysis during drilling. Such analysis is preferable for theapplication discussed hereinabove relating to the real-time receipt ofdrilling parameters during the drilling operation, as described in saidU.S. Pat. No. No. 4,715,451. Alternatively, a time series of vibrationsmay be received and analyzed later, together with such other informationas the received reflections from geophone 18. Such computation may bedone by computer system 19 located at the drilling site, oralternatively may be done by a computing system located remote from thedrilling site, at a time after the drilling is complete, so long as theraw time series data is retained or transmitted.

FIG. 2 illustrates the steps in a method for improving thesignal-to-noise ratio of acoustic vibrations. For purposes of clarity ofdescription, time domain and frequency domain waveforms will be referredto hereinbelow. Referring to FIGS. 3a through 3c, time domainrepresentations of a typical signal as transmitted near drill bit 10,and as detected for both axial and torsional components near the top ofdrill string 4, will be discussed. FIG. 3a illustrates an example ofsignal 22 as generated by, or near, drill bit 10, with signal 22represented in the time domain. This signal is substantially a shortduration wavelet beginning at time t₀ and, for purposes of thisdiscussion, is presumed to generat substantial vibrations both axiallyand torsionally along drill string 4.

For a drill string 4 having a given length between drill bit 10 and thelocation of sub 12, including detectors for both axial and torsionalvibrations, near the surface, the source signal illustrated in FIG. 3awill be detected (process 20 of FIG. 2) at a point in time delayed fromthe generation of the signal. It is known that axial compressionalvibrations have a higher velocity in a pipe structure such as drillstring 4 than do torsional vibrations. In conventional steel drill pipe,for example, the velocity of axial vibrations is approximately 16,850ft/sec, while the velocity of torsional vibrations is approximately10,650 ft/sec. Accordingly, the torsional vibrations will exhibit a timeshift, relative to the axial vibrations induced by the same event,dependent upon this difference in velocity and the length of drillstring 4 between drill bit 10 (or such other apparatus which causes thevibration) and sub 12, at which the vibrations are detected.

The result of the measurement is a time series of vibration amplitudeover time, an example of which is shown in FIG. 3b for axialcompressional vibrations and in FIG. 3c for torsional vibrations. FIG.3b illustrates a time domain representation of detected signal 24a,which begins at a time t_(a), delayed from time t₀ by the length ofdrill string 4 times the axial velocity of vibrations in drill string 4.FIG. 3c similarly illustrates a time t_(b) equal to the torsionalvelocity of vibrations in drill string 4 times the length of drillstring 4. It should be noted that the amplitude of the signals 24a and24b represented in FIGS. 3a and 3b is not necessarily at the same scaleas the source signal, as significant attenuation is likely through drillstring 4.

It should also be noted that the representation of signals 24a and 24bin FIGS. 3b and 3c are not in the form that they would be actuallydetected by detectors in sub 12, but instead separately illustratesignal components 24a and 24b, and noise components 26a and 26b. Ofcourse, the actual time series of the vibrations detected by detectorsin sub 12 would not have the signal and noise components separated asshown in FIGS. 3b and 3c, but would be the sum of the two components 24and 26 for each of the FIGS. For purposes of explanation of this method,however, the two components will be separately illustrated, even thoughin practice, at this step, the shape of the signal component 24 is notknown.

Noise components 26a and 26b, generated from the factors discussedabove, have an amplitude which is quite significant relative to theamplitude of the signal 24a and 24b. While these relative amplitudes areillustrative of the noise problem encountered, it should be noted thatobserved values of the amplitude of the noise components 26 have been onthe order of one thousand times the amplitude of the signal components24; accordingly, the illustrated relative amplitudes of FIGS. 3b and 3care not to scale.

It should also be noted that noise components 26a and 26b are broadbandnoise, i.e., have components at a wide range of frequencies. The noisegenerated along drill string 4 may also have periodic and non-periodiccomponents, depending of course upon the physical cause of theparticular component of the noise. For example, the flow of drilling mudmay generate relatively periodic noise, although at multiple frequenciesand harmonics of such frequencies. Other events, such as casing slap,may not be periodic and will generate noise accordingly. Due to thesefactors, noise components 26, illustrated in FIGS. 3b and 3c for purposeof explanation, may not be representative of actual noise detected bydetectors in sub 12.

This method of noise reduction treats noise components 26a and 26b asrandom noise. Of course, such noise is not truly random, since physicalevents generate the axial and torsional noise vibrations. As will bediscussed below in further detail, the torsional and axial signalcomponents 24 can be treated as proportional to one another at the timesof interest, while the torsional and axial noise components 26 do nothave this relationship. This may be seen intuitively by considering thataxial signal component 24a and torsional signal component 24b areproportional, as generated by the same physical events at the same time,but time shifted as measured due to the velocity difference. On theother hand, axial noise component 26a and torsional noise component 26b,although also generated by same physical events and traveling atdifferent velocities, are generated at points along drill string 4 otherthan that of interest for the signal (i.e., not at drill bit 10). Itwill be seen that by "zooming" in to a particular location of interestsuch as the location of drill bit 10, noise components 26a and 26b willnot coincide with one another, and will appear as random noise in theanalysis.

It should further be noted from a comparison of torsional noisecomponent 26b to axial noise component 26a that, in this example,torsional noise component 26b has a relatively lower amplitude thanaxial noise component 26a. It has been found that it is not uncommon forvibrational noise of one component to have a relatively larger amplitudethan that of another component; of course, depending on the particularsituation, the relative amplitudes of the noise may be substantiallyequal for both the axial and torsional components. As will be describedhereinbelow, this method can take into account such differences in therelative amplitudes of noise components 26a and 26b, in reducing theeffects of such noise in analysis of the desired signal.

It is apparent from a comparison of FIGS. 3b and 3c to each other, andto FIG. 3a, that not only is the noise component 26 significant, butalso that the signal components 24 are distorted from the source signalof FIG. 3a, and distorted differently for axial vibrations relative totorsional vibrations. Referring to FIGS. 4a and 4b, the axial andtorsional frequency responses of a typical drill string 4 to axial andtorsional vibrations, respectively, are shown. Comparison of the axialand torsional frequency response characteristics of FIGS. 4a and 4b willillustrate this differing distortion.

Frequency-dependent Distortion

FIG. 4a shows the frequency response of a drill string 10 tocompressional axial vibrations. The actual data taken for this frequencyresponse characteristic is the response of a drill string 4 consistingof sixteen sections 6 of 31/2 inch pipe, each section approximately 31feet in length. The input used to measure this frequency response is ahammer blow, which easily provides a wide band of frequencies in anabove-ground testing mode. The frequency range for this plot is from 0Hz to 800 Hz, although it should be noted that higher frequencyvibrations generated by the hammer blow impulse will also pass alongsuch a drill string 4, although attenuation of these vibrationsincreases with the frequency of the vibration.

As shown in FIG. 4a, it should be noted that deadbands occur atapproximately 260 Hz, 520 Hz, and 780 Hz. These deadbands result fromreflections of the compressional axial vibrations within a singlesection 6 of drill string 4. It has been observed that where the tooljoints between section of drill string 4 become heavier, the deadbandsbecome wider in frequency and greater in attenuation. One can calculatean approximate base deadband frequency for a single section of pipe bydividing the velocity of compressional axial vibrations (approximately16,000 ft/sec) by twice the length of the section. Accordingly, for asection approximately 31 feet long, the deadband frequencies forcompressional vibrations are at multiples of a frequency on the order of260 Hz. For a drill string 4 having multiple sections 6, each ofapproximately the same length, the deadband frequencies, including thebase deadband frequency and its integral harmonics, will alignsubstantially with each other in the frequency response characteristic,as is evident in FIG. 4a. Based on other measurements, it is believedthat the major deadbands shown in FIG. 4a for axial vibrations (i.e,. atintegral multiples of 260 Hz) are substantially independent of thenumber of sections 6 in the drill string 4, so long as the lengths ofthe sections 6 are substantially the same, as is conventionally the casein the drilling art. It has also been determined that the frequencies ofthe major deadbands to axial vibrations is also substantiallyindependent of the diameter and thickness of the drill pipe of sections6.

Between the major deadband frequencies at multiples of 260 Hz, thefrequency response characteristic of FIG. 4a has pass bands ofrelatively high amplitude. Accordingly, a compressional axial vibrationat a frequency between the deadband frequencies passes along drillstring 4 relatively well. However, between the major deadbands, smallerlocal deadbands and passbands are also present. In the characteristic ofFIG. 4a, the passbands manifest as sixteen peaks in the characteristic.These sixteen peaks correspond to the number of sections 6 in drillstring 4, with the number of local passbands increasing with the numberof sections 6 in drill string 4. It should be noted that the localdeadbands between the major deadbands in the characteristic of FIG. 4aattenuate the vibrations at those frequencies to a lesser degree thanoccurs in the major deadbands.

FIG. 4b illustrates the frequency response characteristic to torsionalvibrations of drill string 4, having sixteen sections 6 of 31/2 inchdrill pipe. Comparison of this characteristic with that of FIG. 4a showsthat the shape of the frequency response characteristic is similar forthe two components of vibration, but that the major deadband frequenciesare different. As discussed above, for a pipe of a given length, thedeadband frequency depends on the length of the pipe and also on thevelocity of the vibrations. Since the velocity of torsional vibrationsis lower than that of axial vibrations, the deadband frequencies for thesame drill string will be lower for torsional vibrations than for axialvibrations. Specifically, the first deadband is in the neighborhood of160 Hz, and at roughly integral multiples there f.

Similarly as in the case of axial vibrational frequency response, it isbelieved that the major deadband frequencies for torsional vibrationsare substantially independent of the size of the pipe and of the numberof sections 6 in drill string 4, so long as the individual lengths ofsections 6 are substantially the same. Also similarly to the axialvibration case, local deadbands and passbands are present in thefrequency response characteristic for torsional vibrations.

Due to the difference in the major deadband frequencies for axial andtorsional vibrations in a drill string 4, the distortion presented to asource signal as it travels along drill string 4 will be different forthe axial component than for the torsional component. This is indicatedby comparison of axial signal component 24a and torsional signalcomponent 24b in FIGS. 3b and 3c, both of which are distorted from thesource signal, and are distorted in different ways relative to oneanother.

Besides the transmission of drill bit energy along drill string 4described hereinabove, other types of information transmitted byacoustic signals along structures such as pipes or conduits are alsoadversely affected by the non-ideal frequency response of the structure.For example, the leakage detection system described in copendingapplication Ser. No. 391,919 determines the location of a crack, orleaky pipe joint, in a pipeline or other conduit by analyzing vibrationsgenerated by the fluid (liquid or gas) escaping through the leak.According to a first embodiment described in application Ser. No.391,919, multiple sets of sensors are placed along the length of thepipe. In the event of a leak occurring between sensors, the differencein arrival time of the vibrations to the sensors on either side thereofdetermines the position of the leak therebetween. In another embodimentdescribed in said application Ser. No. 391,919, the location of the leakis determined by sensing the arrival of both torsional and compressionalvibrations generated by the leak; since the velocities of thesevibrations are different, the difference in arrival time for a signalwill depend upon the distance between the leak and the sensor.

In each of these leakage detection methods, as well as in the cases ofstress wave telemetry and analysis of drill bit energy, the non-idealfrequency response of the pipeline or conduit will distort thevibrational signal being transmitted. In order for the subsequentanalysis of the vibrations to be as accurate as possible, compensationfor the effects of the frequency response of the drill string isdesirable. The following method of deconvolution according to thepreferred embodiment of the invention is intended to compensate forthese effects, and restore the vibrations to the form as originallytransmitted, regardless of the source.

Deconvolution

Referring again to FIG. 2 for the example of analysis of drill bitenergy, after process 20 in which the vibrations are detected bydetectors in sub 12, it is therefore preferable to perform process 30for the removal of the effects of drill string 4 on the transmittedvibrations. Deconvolution of the response of drill string 4 from themeasured axial and torsional vibrations at sub 12 is the preferredmethod for removing these effects, using separate deconvolutionoperators for the axial and torsional components. While process 30,particularly deconvolution of the two signal components 24, is notessential to benefit from the noise reduction method described herein,the difference in distortion for the two vibration components clearlyindicates that separate deconvolution for the two components will beeven further beneficial.

It should be noted that prior deconvolution methods, as noted in theRector, Marion and Widrow paper cited hereinabove, have taken intoaccount only such distortion as results from the ends of the drillstring and the bottomhole assembly, since the frequencies of interest inthose methods are below the first deadband frequency. Such coarsedeconvolution thus only is dependent upon the total length of the drillstring and upon parameters concerning the bottomhole assembly; suchimportant factors as the reflective effects of the tool joints 8 indrill string 4 have not been taken into account by such prior methods.As noted by the above-cited Drumheller article and as evident from thefrequency response characteristics of FIGS. 4a and 4b, drill string 4introduces severe distortion to waves transmitted therethrough,particularly due to the construction of drill string 4 from a number ofsections 6 joined by tool joints 8. Further with reference to FIGS. 4aand 4b, this distortion is especially true for vibrations which are at afrequency above 100 Hz, since such vibrations are subject to the majordeadbands in the characteristics. Accordingly, this preferred embodimentof the invention includes a method for determining a deconvolutionoperator which takes into account the reflective and other distortingeffects of the construction of drill string 4.

It should be noted that the coarse deconvolution noted above, whichtakes into account only the length of drill string 4 and the bottomholeassembly, may be used in the noise reduction technique described herein.It is preferred, however, especially in improving the accuracy of theanalysis of the higher frequency components of the axial and torsionalvibrations, such higher frequency components containing importantinformation in both the drilling parameter monitoring and seismicprospecting applications, that the deconvolution operator be determinedaccording to the preferred embodiment of the invention describedhereinbelow.

Furthermore, as is evident from the representations of FIGS. 3b and 3c,and as will be made further evident hereinbelow, the value of the timedelays t_(a) for axial vibrations and t_(b) for torsional vibrations areimportant in the noise reduction method described herein. Such timedelays are also important in the application of pipeline leak detection,since the location of the leak is determined from prior knowledge of thevelocity of the vibrations and arrival time differences between sensors,and between types of vibrations (axial and torsional, for example).

Referring to FIG. 5, a method of deconvolution according to thepreferred embodiment of the invention, and in which the deconvolutionoperators retain these time delay values, will now be described. Theretained time delay values are beneficial in the subsequent operationsof reducing the effects of the random noise, in the distancecalculations for leakage detection, and in reducing the number of pointsin performing the Fast Fourier Transform required in the deconvolutionprocess.

As noted above, the frequency response of drill string 4 may be knownfrom experimentation or modeling; FIGS. 4a and 4b illustrate themagnitude of the frequency response (phase is not illustrated). Apreferred method for acquiring the response for drill string 4 is by wayof applying vibrational signals at the top of drill string 4, forexample with a hammer blow (i.e., substantially an impulse input) orwith some other wideband stimulus, to present an axial vibrational inputinto drill string 4. These vibrations will travel downhole along drillstring 4, and reflect from the distal end thereof (e.g., at drill bit10) back to the surface. Detectors such as in sub 12 describedhereinabove detect the transmitted vibrations, with the detectedvibrations used to determine the response of drill string 4 to the axialvibrations generated by the axial hammer blow (of course, accounting fortravel in both directions). Torsional vibrations may be applied by ahammer blow to a flange located near the top of drill string 4, in adirection which produces torsional vibrations along drill string 4, suchvibrations also traveling down drill string 4, reflecting from drill bit10 and traveling back up drill string and detected by the detectors insub 12. After analysis, a representation of the response of drill string4 is stored by conventional computing equipment. Referring to FIG. 5,process 31 indicates the retrieval of the axial vibration frequencyresponse I_(a) (f) and torsional vibration frequency response I_(b) (f)from the memory of the computing equipment performing the methodaccording to this embodiment of the invention.

The values of the time delays are preferably combined with the FFTs ofthe impulse response operators, according to this embodiment of themethod. Such retention of the time delay values with the frequencyresponse is preferred, as this representation is stored in the computingequipment performing the analysis, and is used repeatedly over time asthe measured vibrations are monitored and analyzed. Time delay in thefrequency domain, as is well known in the art, is expressed bymultiplication by the phase shift terms. In this embodiment, these phaseshift terms may be expressed as exp(-jt_(a) 2πf) and exp(-jt_(b) 2πf)for the axial and torsional cases, respectively. In this embodiment ofthe deconvolution operation, the complex frequency response of drillstring 4 is thus expressed as:

    I.sub.a (f, t.sub.a)=F[i.sub.a (t-t.sub.a)]=[I.sub.a (f)][exp(-jt.sub.a 2πf)]

    I.sub.b (f, t.sub.b)=F[i.sub.b (t-t.sub.b)]=[I.sub.b (f)][exp(-jt.sub.b 2πf)]

where i_(a) (t-t_(a)) and i_(b) (t-t_(b)) are the time-shifted timedomain impulse responses for axial and torsional vibrations,respectively, where F is the Fourier operator, and where I_(a) (f) andI_(b) (f) are the complex Fourier transforms of the impulse response foraxial and torsional vibrations, respectively. FIG. 5 illustrates theperforming of this operation in process 32.

It should of course be noted that, if the distance between sub 12containing the detectors and the source of the signal is constant formultiple deconvolution operations, the result of process 32 may bestored in lieu of the non-time-shifted frequency responsecharacteristics. It is contemplated, however, that the distance betweensub 12 containing the detectors and the point at which the signal is tobe analyzed may change over time. For example, the analysis may wish to"zoom" in on another location of drill string 4 for analysis of thesignal coming therefrom. Also, the addition of sections 6 to drillstring 4 as drilling progresses will also change the distance betweendrill bit 10 and sub 12, and accordingly the time delay values andresponse characteristics. For ease in performing such operations withvarying delay times t_(a) and t_(b), it is preferable to store andretrieve the frequency response characteristic, and to multiply each bythe exponential phase shift term during the deconvolution.

In the context of leakage detection, it is also preferable that thefrequency response characteristic be stored and retrieved separately,with the exponential phase shift term applied thereto during thedeconvolution. This allows the leakage detection method to iterativelychange the time delays for the axial and torsional vibrations, so thatthe location of the leakage can be identified by correlation of theaxial and torsional vibrations, after deconvolution. Identification ofthe time delay values corresponding to the best correlation willidentify the location of the leakage.

For purposes of explanation, the axial and torsional vibrations areexpressed as time functions m_(a) (t) for the measured axial vibrations,and m_(b) (t) for the measured torsional vibrations, with the functionsextending over all non-negative time t>0. As noted above, each of thesetime series can be considered as the sum signal and noise components, asfollows:

    m.sub.a (t)=s.sub.a (t)+n.sub.a (t)

    m.sub.b (t)=s.sub.b (t)+n.sub.b (t)

where s(t) and n(t) are the time domain representations of the signaland noise components, respectively, of the measured time series signalsm(t).

In FIG. 5, retrieval of the time series m_(a) (t) and m_(b) (t) frommemory of the computer, or directly from the measurement apparatus, isindicated by process step 33. Since convolution in the time domainrequires integration, but only requires multiplication (or division, inthe case of deconvolution) in the frequency domain, Fouriertransformation of the measured time series of signals into the frequencydomain is preferred, and is performed in process 34 of FIG. 5.

Since the frequency response operators separately retain the informationrelating to the time delay values t_(a) and t_(b), the FFTs for thefrequency response may be done over a limited number of points in time.This is useful due to the limited number of points that many FFTalgorithms (and hardware) can handle within reasonable computing time,making it useful to limit the range of points in time that are used inthe FFT. Accordingly, in storing the axial frequency response, thepoints used in the FFT can begin at or closely before the time t_(a) ;similarly, in storing the torsional frequency response, the points usedin the FFT can begin at or closely before the time t_(b). Since the timedelay values are incorporated into the expressions hereinabove forfrequency response of drill string 4, they need not be maintained in theFFT of the frequency response. The expressions for the frequency domainrepresentations of the measured vibrations are as follows:

    M.sub.a (f)=F[m.sub.a (t)]

and

    M.sub.a (f)=F[m.sub.a (t)]

where M_(a) (f) is the frequency domain representation of the measuredaxial vibrations, where M_(b) (f) is the frequency domain representationof the measured torsional vibrations, and where F is the Fouriertransform operator.

Deconvolution is then accomplished, in process 35 of FIG. 5, by thedivision of the frequency domain representations M_(a) (f) and M_(b) (f)by the frequency response operators I_(a) (f,t_(a)) and I_(b) (f,t_(b)),respectively. This division is preferably done according to the wellknown technique of point-by-point division of the two representations ata series of discrete frequencies in the range of interest. In order toavoid divide-by-zero problems, it is preferred to add "white noise",i.e., small magnitude signals at all frequencies, to the representationsof the frequency response operators I(f,t). The results of thesedivision operations are then converted into time domain representationsby performing the inverse FFTs, in process 36 of FIG. 5, resulting intime domain representations m'_(a) (t) and m'_(b) (t). The sum of theserepresentations of signal and noise components can be expressed asfollows:

    m'.sub.a (t)=s'.sub.a (t)+F.sup.-1 [N.sub.a (f)/I.sub.a (f)exp(-jt.sub.a 2πf)]

    m'.sub.b (t)=s'.sub.b (t)+F.sup.-1 [N.sub.b (f)/I.sub.b (f)exp(-jt.sub.b 2πf)]

where F⁻¹ is the inverse Fourier operator, and where N(f) is thefrequency domain representation of noise components 26.

Referring to FIGS. 6a and 6b, representations m'_(a) (t) and m'_(b) (t)after deconvolution are illustrated for the axial and torsional measuredvibrations, respectively, with noise components 26' and signalcomponents 24' shown separately as above. As a result of thedeconvolution of process 30, the signal components 24a' and 24b' moreclosely resemble one another, and more closely resemble the sourcesignal 22 of FIG. 3a. This is due to the removal of the effects of drillstring 4 on the vibrations transmitted through drill string 4 from thepoint of interest (e.g., drill bit 10 to the detectors in sub 12. Thetime delay values t_(a) and t_(b) have been retained after thedeconvolution, as discussed hereinabove, as shown in FIGS. 6a and 6b.

It should be noted that the deconvolution step described above willoperate on both the noise and signal components of the measured timeseries of vibrations. However, since for purposes of the noise reductionmethod this noise is considered as random noise, the deconvolution ofrandom noise results in random noise, which is equally reducibleaccording to the method described herein.

Time-Shift for Signal Reinforcement

The remainder of the method of noise reduction in the analysis of drillbit-generated acoustic vibrations will now be described in furtherdetail.

Referring again to FIG. 2, in the case of analyzing the source signatureof the drill bit energy, upon the completion of the deconvolution ofprocess 30, the next step in the noise reduction method is a time shiftof the deconvolved axial and torsional time domain representationsm'_(a) (t) and m'_(b) (t) relative to one another. This is performed inprocess 40 of FIG. 2.

Referring again to FIGS. 6a and 6b, it should be noted that the signalcomponents 24a' and 24b' more closely resemble one another, with thetorsional component 24b' delayed in time from the axial component 24a'by the time t_(b) -t_(a) ; no such resemblance is present for the noisecomponents 26' since, as discussed above, the noise signals aregenerated at various points along drill string 4, so that the time delaybetween the arrival of the axial noise component 26a' and the torsionalnoise component 26b' will not be a constant for all such noise, but willdepend upon the individual noise source, many of which are summedtogether when considering the signal components 24' of interest.

This method takes advantage of the correlation between the signalcomponents 24' and the lack of correlation between the noise components26' to reduce the effects of the noise on the signal. This is done inprocess 40, where the two representations m_(a) (t) and m_(b) (t) aremade coincident in time and then summed.

In practice, of course, the representations m'_(a) (t) and m'_(b) (t)are time series of measured vibrations, upon which the operations ofprocess 30 have been performed, and the signal and noise components 24'and 26' are not known. However, the distance from drill bit 10 (or suchother source of interest) is known, as are the relative velocities ofthe torsional and axial vibrations in drill string 4. Accordingly, thetime shift of process 40 can be easily done by multiplying the distancebetween drill bit 10 and sub 12, in this example, by the difference inthe axial and torsional velocities to determine the value t_(b) -t_(a).Once t_(b) -t_(a) has been determined, either the axial or torsionaltime series can be shifted by this value in the computer performing theanalysis. In this example, the representation of the torsionalvibrations will be shifted to be considered earlier in time; the shiftedrepresentation will be referred to as m'_(b) (t-(t_(b) -t_(a))).Referring to FIGS. 7a and 7b, the time shifting of the torsionalrepresentation m'_(b) (t-(t_(b) -t_(a))) is illustrated, with timeshifted signal component 24b" and time shifted noise component 26b". Itshould be noted, of course, that the axial representation mayalternatively be shifted later in time to coincide with the torsionalrepresentation, if desired; further alternatively, both representationsmay be shifted in time to coincide at a third point in time.

By virtue of the assumption that the axial and torsional signalcomponents 24 are similar, or substantially proportional to one another,the two time-shifted (and deconvolved, if desired) representations maybe summed together to reinforce the signal portions. It is believed thatthis assumption is valid in at least the cases of vibrations generatedby drill bit 10, vibrations generated by casing slap, and vibrationsgenerated by axial and torsional transducers located in a bottomholeassembly 11 for the application of stress wave telemetry. Therefore,upon completion of the time shift of process 40, the two representationsm'_(a) (t) and m'_(b) (t-(t_(b) -t_(a))) are summed together in process50. Since the signal components 24a' and 24b" resemble one another, andsince the noise components 26a' and 26b" do not (both being random,including after the time shift of the torsional representation), such asummation will tend to reinforce the signal components 24 while thenoise components 26 will randomly add to or subtract from one another.Accordingly, the signal-to-noise ratio will be improved, with the signalcomponents 24 reinforcing one another relative to the noise components26 which will remain approximately the same, on the average over thetime period of interest. The summing operation, in the case where thetorsional representation is time-shifted, can be expressed as follows:##EQU1## However, as recognized above, the time-shifted torsional signalcan be considered as proportional to the axial signal, i.e.,

    s'.sub.b (t-(t.sub.b -t.sub.a))=Ks'.sub.a (t)

Accordingly, the sum of the axial and time-shifted oomponents canexpressed as follows:

    m'.sub.a (t)'m'.sub.b (t-(t.sub.b -t.sub.a))=(K+1)s'.sub.a (t)+n'(t)

where n'(t) is a noise component consisting of the sum of thedeconvolved axial and time-shifted torsional noise components. As notedhereinabove, since the noise components can accurately be considered asrandom for purposes of this method, the factors making up n'(t) need notbe retained.

It should be noted that the time shifting operation of process 40 may bedone in conjunction with the summation of process 50, rather than as aseparate step prior to the summation, if the computing process is moreeasily done in this way. For example, if the number of samples in thetime series of measured vibrations are the same for the axial andtorsional vibrations, an ordered summation may be done merely by addingthe amplitude of the first axial sample (at about time t_(a)) with thefirst torsional sample (at about time t_(b)), continuing over the rangeof time of interest. Such a method would necessarily incorporate thetime shift, since the vibrations would coincide in time due to thesummation operation performed, and without an additional step oftime-shifting performed for one of the time series of measuredvibrations.

It should also be noted that the signal-to-noise ratio is improved bythis method. Considering the signal-to-noise ratio of each of the axialand torsional components, as measured, as follows:

    S/N.sub.a =s.sub.a (t)/n.sub.a (t)

    S/N.sub.b =s.sub.b (t)/n.sub.b (t)

the signal-to-noise ratio after the method has been performed thus canbe on the order of K+1 times that each of the original ratios, if theassumption that there is, on the average, no additive reinforcement ofthe noise components in the summation so that the amplitude of the noisecomponents remains relatively constant. For the case where theamplitudes of the noise components in the axial and torsional vibrationsare approximately equal, it is believed that the improvement in thesignal-to-noise ratio is on the order of the square root of two.

It shoudl further be noted, however, that the amplitude of the axialnoise component n_(a) (t) is generally significantly larger than theamplitude of the torsional noise component n_(b) (t), as in mostdrilling applications more axial noise than torsional noise isgenerated. Accordingly, the increase in the signal-to-noise ratio can bemaximized if the amplitude of the noise components are approximately thesame prior to the summation operation in process 50. This can beaccomplished be performing a weighted summation where one of thecomponents, generally the torsional component, has its amplitudemultiplied by a constant which is the ratio of the amplitude of theaxial noise to the ratio of the torsional noise.

the summing operation would be as rollows:

    m'.sub.a (t)+m'.sub.b (t-(t.sub.b -t.sub.a))=[s'.sub.a (t)+n'.sub.a (t)]+(N.sub.a /N.sub.b)[s'.sub.b (t-(t.sub.b -t.sub.a))+n'.sub.b (t-(t.sub.b -t.sub.a))]

where n'(t) represents the deconvolved noise components, as describedhereinabove, and where N_(a) and N_(b) represent the root-mean-squareamplitude of the axial and torsional noise components, respectively,over the time period of interest. This weighted summation is preferablein the case where the relative amplitudes of the noise components differbetween the axial and torsional vibrations, as it provides the abilityof the two noise components to cancel out one another to a greaterextent than in the case where one is much larger than the other. Suchcancellation is, of course, helpful in improving the signal-to-noiseratio.

The result of the weighted (or unweighted, as the case may be) summationis a signal in which the signal component can be more easily identifiedand analyzed for the particular operation. Referring to FIG. 2, the caseof seismic prospecting using drill bit 10 as the source is completed byprocess 60, in which the source signal is correlated with the reflectedsignals detected by geophone 18 of the system of FIG. 1. Methods ofperforming such correlation are conventional in the art, and include,for example, the Vibroseis®) technique. For purposes of performing suchcorrelation, the time delay resulting from transmission of thevibrations along drill string 4 must, of course, be taken into account.A method for performing such correlation, in the particular case wherethe drill bit energy serves as the seismic source waves, is described inthe Rector, Marion and Widrow article "Use of Drill-Bit Energy as aDownhole Seismic Source" cited hereinabove.

In the application described in U.S. Pat. No. 4,715,451 citedhereinabove where the sensed vibrations are indicative of certaindrilling parameters, the method described hereinabove facilitatesidentification and analysis of the sensed vibrations, to a much greaterdegree than where the signal-to-noise ratio remains low. In addition, bychanging the distance of interest, i.e., changing the value of time usedin the relative time shift between the axial and torsional vibrationsafter deconvolution, different locations of drill string 4 can beseparately analyzed. This allows analysis of the vibrations originatingat any point along drill string 4, and allows for the detection of thelocation of casing slap or other vibration generating events, withoutrequiring additional steps of detecting the vibrations; the originallydetected time series data can be used, and reanalyzed, with the changein the relative time delay.

In addition, the improved signal-to-noise ratio provided by the methoddescribed hereinabove enhances the ability to analyze and use datatransmitted by vibrations along a structure such as a drill string. Suchimprovement in the definition of the signal components of the vibrationsallows for better quantification of drilling parameters, to determinesuch parameters as in the example of the above-referenced U.S. Pat. No.4,715,451.

The sensing and interpretation, at the surface, of drilling vibrationsgenerated downhole can be an important technique in the real-timecontrol of the drilling operation, including the real-time control ofthe drilling operation to avoid failures. For example, vibrationsindicative of the RPM and weight-on-bit parameters can be monitored, sothat resonant drilling conditions can be detected and the drillingprocess modified as necessary to avoid such resonant conditions. Inaddition, impact of the casing on the sides of the wellbore generatesparticular vibrations which can be detected in the drill string at thesurface; the above-described method can be used to determine thelocation of the drill string interaction with the wellbore sides, sothat adjustment of drilling parameters to preclude eventual failure dueto such interaction can be made. The leak detection method describedhereinabove, where vibrations of the drill string indicative of fluidpassing through a leak are monitored, can also be applied to thedrilling operation, so that necessary repairs can be made prior to adisastrous wash-out. The vibrational information from the drillingoperation, sensed and interpreted at the surface, can also be used fordrilling optimization, particularly relative to the formation typeencountered by the drill bit in real-time.

Furthermore, the improved signal-to-noise ratio, and also the improveddeconvolution technique, allows for more accurate determination of theseismic source signature in the application of seismic prospecting usingthe drill bit as the seismic source. Since the accuracy of thecorrelation results depends upon the accuracy of the seismic sourcesignature, the accuracy of the seismic analysis will be improved by useof the method described herein. Furthermore, currently available systemsfor detecting the seismic source signature from drill string vibrationshave been observed to be ineffective for particular drilling operations,such as those using PDC bits and downhole motors, because the noiseamplitude is apparently larger for these operations. It should be notedthat the choice of drill bit, and the choice of downhole motor versustop drive, depends in large part upon the type of formations into whichthe drilling is occurring. Accordingly, the method described herein canenable seismic prospecting in such formations which require the use ofsuch drilling equipment, as the method provides for reduction of theeffects of noise in the vibrations transmitted alon the drill string.

Stress Wave Telemetry Deconvolution

The method also provides improvement in the vibration signals receivedin stress wave telemetry so that the accuracy of stress wave telemetrycommunication is improved. In addition, since a higher degree ofattenuation can be tolerated with an improved signal-to-noise ratio,this method also enables stress wave telemetry transmission at higherfrequencies and data rates.

In stress wave telemetry, deconvolution using the frequency response ofthe pipe may be performed in such a manner as to take advantage of theprior knowledge of the frequencies at which the information is beingtransmitted. FIG. 9 illustrates a flow diagram for the deconvolution ofstress wave telemetry information, in the example where the informationis frequency shift keyed.

Referring now to FIG. 9, process 30' for the deconvolution of stresswave telemetry data will now be described. Conventional computingequipment, such as described relative to FIG. 8 hereinabove, can beprogrammed to perform the calculations and operations in the flow ofFIG. 9. It should be noted that process 30' of FIG. 9 is applicableseparately to axial and torsional vibration data, utilizing the axialand torsional frequency response of drill string 4 illustrated in FIGS.4a and 4b described hereinabove.

Similarly as described hereinabove, the frequency response of the drillstring I(f) is retrieved from memory in process 71. Since deconvolutionin the time domain corresponds to division in the frequency domain, andsince process 30' performs the deconvolution by way of a convolutionoperation (as will be described hereinbelow), the reciprocal of thefrequency response I(f) is calculated in process 73. It is preferable toeliminate the potential for divide-by-zero problems by adding a smalllevel of "white noise" to the frequency response characteristic I(f)prior to its division into unity. Accordingly, the reciprocal frequencyresponse characteristic A(f) may be calculated in process 73 as:

    A(f)=1/[I(f)+e]

where e is a small constant relative to the amplitude of I(f), and isindependent of frequency. Such division may be done in conventionalcomputing equipment in the conventional manner, for example by iterativeaddition and division at a series of desired frequency values.

Since the frequencies of transmission are known in the stress wavetelemetry application, the frequency response of drill string 4 outsideof the transmission frequencies is neither useful nor relevant in thedeconvolution process 30'. Accordingly, in process 75, the reciprocalfrequency response A(f) calculated in process 71 is bandpass filteredabout the frequencies of transmission. For example, if frequency shiftkeyed (FSK) digital data is being transmitted by vibrations at 920 Hz(for a "0") and at 1180 Hz (for a "1"), the reciprocal frequencyresponse A(f) can be filtered so that frequencies near the transmissionfrequencies (e.g., plus or minus 50 Hz from each of the transmissionfrequencies) will be passed with unity gain, with frequencies outside ofthe bands fully attenuated by the filter. The result of process 75 isthus a filtered reciprocal frequency response B(f):

    B(f)=bandpass[A(f), 870-970 Hz, 1130-1230 Hz]

where the bandpass function, performed by computing system 19, is aconventional digital bandpass filter as can be performed by conventionalcomputing equipment. It should be noted that the DSP boards discussedhereinabove are also especially adapted for the performing of digitalfilter operations, as is well known in the art.

Process 77 calculates the inverse Fourier transform of the bandpassedreciprocal frequency response B(f) in the conventional manner. Theresult is a time domain operator b(t), which represents the reciprocalof the impulse response of drill string 4, at frequencies near thetransmission frequencies of the FSK data. It may be useful to furtherfilter the time domain operator b(t) in such a manner that only theportions thereof which are above a certain amplitude are used in theconvolution operation, with the lower amplitude portions set to zero;such filtering will reduce the number of calculations in the convolutionoperation with minimal effect on the result.

In process 74, the time series data m(t) upon which the deconvolutionoperation is to be performed is retrieved from process 20 of FIG. 2.Such time series data can, of course, be received directly from sub 12,may be alternatively retrieved from the memory of computing system 19 ifpreviously received data is to be analyzed, or may be received from suchother appropriate source. Process 78 performs a time domain convolutionof the time series data m(t) with the reciprocal filtered impulseresponse operator b(t). Since the operator b(t) is derived from thereciprocal of the frequency response, the time domain convolution ofprocess 78 corresponds to deconvolution with the impulse response ofdrill string 4. The result of process 74 is thus a time series m'(t)which, as in the case of process 30 described hereinabove, is themeasured vibration data with the distortions from the non-idealtransmission of drill string 4 removed therefrom.

It should be noted that, for repeated transmissions at constantfrequencies from the same location in drill string 4, the result b(t)from processes 71, 73, 75, and 77 may be stored in the memory ofcomputing system 19 for convolution with multiple time series m(t) overthe length of the transmission. This is possible due to the dependenceof operator b(t) solely on the construction of drill string 4 betweenthe transmitting and receiving locations, and on the frequency oftransmission. Accordingly, the deconvolution of process 30' can be mostefficiently performed by computing system 19 by avoiding recalculationof the repetitive steps.

FIGS. 10a and 10b illustrate the effect of deconvolution according tothis embodiment of the invention on data received via stress wavetelemetry. FIG. 10a illustrates a decoded timedomain signal transmittedaxially along a drill string of 32 31-foot sections of standard drillpipe, where FSK modulated digital information is being transmitted asaxial compressional vibrations. In this example, the "0" data state istransmitted at 920 Hz, and the "1" data state is transmitted at 1180 Hz,with the width of each bit being 1/50 second. In FIGS. 10a and 10b, thetwo decoded signals are illustrated after cross-correlation with aHanning windowed sine function (at 920 Hz and 1180 Hz, respectively)having a length of 1/50 second, corresponding to the bit width, andafter further processing by calculating the envelope of the resultaccording to well known techniques. The 920 Hz signal is shown as adashed line, and the 1180 Hz signal as a solid line, in FIGS. 10a and10b.

FIG. 10b illustrates the result of deconvolution according to thisembodiment of the invention. In this example, the frequency response ofthe drill pipe was determined by the application of axial vibrationsusing a transducer as described in copending applications Ser. No.554,030, and Ser. No. 554,022 cited hereinabove, to generate broadbandvibrations. The generated axial vibrations were then sensed at one endof the pipe, to arrive at a frequency response, exhibiting similarbehavior as that shown in FIG. 4a discussed hereinabove.

In performing the method illustrated in FIG. 9, on the data of FIG. 10a,the frequency response was digitized to approximately 8192 points. Afterapplication of the white noise as noted hereinabove, the reciprocalfunction β(f) was generated and stored, and an inverse FFT was performedon the 8 k points. It was observed that the portions of the inverse FFTresult at the opposite extremes in time were of little interest, whichallowed reduction of the number of points in the inverse FFT toapproximately 1 k points. Deconvolution of the time-domain waveform ofFIG. 10a was then performed according to conventional techniques. Afterapplication of the Hanning window sine function and further processing,as noted hereinabove, the result of the deconvolution of the time seriesdata of FIG. 10a according to this method is illustrated in FIG. 10b.

Comparison of FIG. 10b to 10a illustrates that usable FSK modulatedinformation is severely distorted by the non-ideal frequency response ofthe drill string, to the extent that some of the data bits at 1180 Hz donot cross the threshold of detectability. The deconvolution methodaccording to this embodiment of the invention, however, allows such databits to have good amplitude, and accordingly to convey meaningful data.The present invention thus greatly facilitates use of stress wavetelemetry, as described in copending applications Ser. No. 188,231, Ser.No. 554,030, and Ser. No. 554,022, particularly at higher frequencies.

It should be noted that the methods described herein are applicable notonly to axial and torsional vibrations transmitted along a drill stringor other structure, but may also be applied to other acoustic signalstransmitted or traveling along a structure, where such signals aregenerated at a particular location and have components of differingvelocities which are substantially proportional to one another.

While the invention has been described herein relative to its preferredembodiments, it is of course contemplated that modifications of, andalternatives to, these embodiments, such modifications and alternativesobtaining the advantages and benefits of this invention, will beapparent to those of ordinary skill in the art having reference to thisspecification and its drawings. It is contemplated that suchmodifications and alternatives are within the scope of this invention asclaimed hereinbelow.

I claim:
 1. A method for reducing the effects of frequency-dependentdistortion on vibrations generated at a first location of a structureand detected over time at a second location, said detected vibrationsrepresented as a first time series corresponding to vibrations having afirst transmission velocity along said structure and a second timeseries corresponding to vibrations having a second transmission velocityalong said structure, said method comprising:storing a first frequencyresponse characteristic for said vibrations having a first transmissionvelocity along said structure; storing a second frequency responsecharacteristic for said vibrations having a second transmission velocityalong said structure; retrieving the values of said time series over atime interval; combining said first frequency response characteristicwith a first time delay value to arrive at a first deconvolutionoperator; combining said second frequency response characteristic with asecond time delay value to arrive at a second deconvolution operator;wherein the product of said first velocity and said first time delayvalue is approximately the same as the product of said second velocityand said second time delay value; and deconvolving said retrieved timeseries values with deconvolution operator.
 2. The method of claim 1,further comprising:performing a Fourier transform on said retrieved timeseries values, prior to said deconvolving step.
 3. The method of claim2, wherein said deconvolving step comprises:dividing the transformedretrieved time series values by said deconvolution operator.
 4. Themethod of claim 3, further comprising:performing an inverse Fouriertransform on the result of said dividing step.
 5. The method of claim 1,wherein said retrieving step comprises:retrieving the values of saidfirst time series over a time interval; and retrieving the values ofsaid second time series over a time interval; wherein the time intervalsof said first and second time series are shifted in time relative to oneanother by the difference of said first and second time delay values. 6.A method for reducing the effects of frequency-dependent distortion onvibrations generated at a first location of a structure and detectedover timea t a second location, said detected vibrations represented asa first time series corresponding to vibrations having a firsttransmission velocity along said structure and a second time seriescorresponding to vibrations having a second transmission velocity alongsaid structure, said method comprising:storing a first frequencyresponse characteristic for said vibrations having a first transmissionvelocity along said structure; storing a second frequency responsecharacteristic for said vibrations having a second transmission velocityalong said structure; combining said first frequency responsecharacteristic with a first time delay value to arrive at a firstdeconvolution operator; combining said second frequency responsecharacteristic with a second time delay value to arrive at a seconddeconvolution operator; wherein the product of said first velocity andsaid first time delay value is approximately the same as the product ofsaid second velocity and said second time delay value and wherein thetime intervals of said first and second timer series are shifted in timerelative to one another by the difference of said first and second timedelay values; retrieving the values of said first and second time seriesover a time interval; deconvolving said retrieved time series valueswith said deconvolution operator; and storing new values for said firstand second time delay values, said new values correspondign to a newdistance along said structure.
 7. The method of claim 1, furthercomprising:generating said vibrations at said first location of saidstructure; and sensing vibrations at said second location of saidstructure.
 8. The method of claim 1, wherein said vibrations aregenerated by fluid passing through a leak in said structure at saidfirst location.
 9. The method of claim 1, wherein said structurecomprises a drill string;and wherein said vibrations are generated by adrill bit at an end of said drill string.
 10. A method for deconvolutionof acoustic signals transmitted along a pipe structure, comprising thesteps of:storing the frequency response of said pipe structure; storinga first time series corresponding to vibrations having a first velocityin said pipe structure and a second time series corresponding tovibrations having a second velocity in said pipe structure; storingfirst and second time delay values, said first and second time delayvalues, multiplied by said first and second velocities, corresponding toa distance between first and second locations of said structure;combining said frequency response and said time delay value to generatefirst and second deconvolution operators; deconvolving said first timeseries with said first deconvolution operator, and said second timeseries with said second deconvolution operator.
 11. The method of claim10, wherein said frequency response is in the frequency domain.
 12. Themethod of claim 10, further comprising:performing the Fourier transformof said time series; and wherein said deconvolving step comprisesdividing the Fourier transform of said time series by said deconvolutionoperator.
 13. The method of claim 10, further comprising:generating saidvibrations at said first location of said structure; and sensingvibrations at said second location of said structure.
 14. The method ofclaim 10, further comprising:analyzing the results of said deconvolvingsteps; and storing new values for said first and second time delayvalues.
 15. The method of claim 10, wherein said vibrations aregenerated by fluid passing through a leak in said structure at saidfirst location.
 16. The method of claim 10, wherein said structurecomprises a drill string;and wherein said vibrations are generated by adrill bit at an end of said drill string.